{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "bc5ba216",
   "metadata": {},
   "source": [
    "Ce script permet, à partir d'un tableau force/déplacement et de données géométriques issus d'un essai de traction uniaxiale, de tracer la courbe contrainte/déformation puis de fitter une loi hyperélastique sur cette courbe."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b7881312",
   "metadata": {},
   "source": [
    "Dans un premier temps, on récupère les données expérimentales pour en extraire une courbe contrainte ingénieur (contrainte PK1)/allongement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "48f62e54",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tableau de données :\n",
      " [[  0.       2.33  ]\n",
      " [  0.4484   2.87  ]\n",
      " [  0.9117   3.13  ]\n",
      " [  1.5094   2.85  ]\n",
      " [  2.0475   3.39  ]\n",
      " [  2.4809   4.2   ]\n",
      " [  2.9293   4.74  ]\n",
      " [  3.4673   4.73  ]\n",
      " [  3.6317   4.73  ]\n",
      " [  4.1549   6.36  ]\n",
      " [  4.5435   7.45  ]\n",
      " [  5.1712   8.26  ]\n",
      " [  5.5747   7.98  ]\n",
      " [  6.1726   9.88  ]\n",
      " [  6.5464  11.52  ]\n",
      " [  6.92    11.51  ]\n",
      " [  7.3087  13.42  ]\n",
      " [  7.7571  15.05  ]\n",
      " [  8.2501  17.5   ]\n",
      " [  8.6691  19.41  ]\n",
      " [  9.0428  20.49  ]\n",
      " [  9.3866  22.13  ]\n",
      " [  9.7604  24.58  ]\n",
      " [ 10.1192  26.21  ]\n",
      " [ 10.5527  28.39  ]\n",
      " [ 10.8967  31.39  ]\n",
      " [ 11.1808  33.57  ]\n",
      " [ 11.6292  34.93  ]\n",
      " [ 11.9582  37.93  ]\n",
      " [ 12.2723  41.21  ]\n",
      " [ 12.6611  43.93  ]\n",
      " [ 12.9901  47.21  ]\n",
      " [ 13.4237  50.21  ]\n",
      " [ 13.648   52.12  ]\n",
      " [ 13.9172  54.02  ]\n",
      " [ 14.1865  58.39  ]\n",
      " [ 14.4706  60.57  ]\n",
      " [ 14.6502  64.39  ]\n",
      " [ 14.9942  69.94  ]\n",
      " [ 15.383   71.49  ]\n",
      " [ 15.6673  75.85  ]\n",
      " [ 15.9067  79.68  ]\n",
      " [ 16.2058  82.95  ]\n",
      " [ 16.4752  87.59  ]\n",
      " [ 16.7893  90.86  ]\n",
      " [ 16.9988  95.51  ]\n",
      " [ 17.2532  99.05  ]\n",
      " [ 17.5225 103.97  ]\n",
      " [ 17.8666 108.88  ]\n",
      " [ 18.0763 114.61  ]\n",
      " [ 18.3756 120.07  ]\n",
      " [ 18.615  124.44  ]\n",
      " [ 18.8844 129.36  ]\n",
      " [ 19.1239 134.82  ]\n",
      " [ 19.3185 138.64  ]\n",
      " [ 19.5131 143.01  ]\n",
      " [ 19.7076 146.56  ]\n",
      " [ 19.9172 150.92  ]\n",
      " [ 20.0671 157.48  ]\n",
      " [ 20.3216 162.94  ]\n",
      " [ 20.4863 167.86  ]\n",
      " [ 20.7259 174.14  ]\n",
      " [ 20.9953 180.14  ]\n",
      " [ 21.2349 186.15  ]\n",
      " [ 21.4895 193.52  ]\n",
      " [ 21.6543 198.98  ]]\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# -*- coding: utf-8 -*-\n",
    "\"\"\"\n",
    "Created on Tue Jan 30 17:28:54 2024\n",
    "\n",
    "@author: abrunon\n",
    "\"\"\"\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import curve_fit\n",
    "\n",
    "#Données d'entrée\n",
    "epaisseur = 1.63\n",
    "largeur = 23\n",
    "L0 = 63\n",
    "\n",
    "section_init = epaisseur*largeur\n",
    "\n",
    "# Spécifiez le chemin vers votre fichier texte\n",
    "chemin_fichier = 'force_deplacement_aorte.txt'\n",
    "\n",
    "# Charger les données à partir du fichier texte dans un tableau\n",
    "donnees_tableau = np.loadtxt(chemin_fichier)\n",
    "\n",
    "# Afficher le tableau de données\n",
    "print(\"Tableau de données :\\n\", donnees_tableau)\n",
    "depl = donnees_tableau[:,0]\n",
    "force = donnees_tableau[:,1]\n",
    "\n",
    "plt.scatter(depl, force, label='Données expérimentales brutes')\n",
    "plt.legend()\n",
    "plt.xlabel('Déplacement (mm)')\n",
    "plt.ylabel('Force (N)')\n",
    "plt.show()\n",
    "\n",
    "# Allongement\n",
    "allong = 1+depl/L0\n",
    "\n",
    "# Contrainte ing\n",
    "stress_ing = force/section_init\n",
    "\n",
    "# Tracé des données expérimentales à fitter\n",
    "\n",
    "x_data = allong\n",
    "y_data_exp = stress_ing\n",
    "\n",
    "plt.scatter(x_data, y_data_exp, label='Données expérimentales')\n",
    "plt.legend()\n",
    "plt.xlabel('Allongement (-)')\n",
    "plt.ylabel('Contrainte de PK1 (MPa)')\n",
    "plt.title('Ajustement de fonction aux données expérimentales')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "583683d4",
   "metadata": {},
   "source": [
    "Il faut maintenant établir l'équation qui permettra de fitter cette courbe, à partir de la théorie hyperélastique.\n",
    "Voici la démonstration : \n",
    "### **Démonstration en quasi-incompressible avec pression explicite (dépendance en $I_1$, $I_2$, et $J$)**\n",
    "\n",
    "Nous considérons un matériau hyperélastique **quasi-incompressible**, pour lequel la condition $J \\approx 1$ est imposée via une pression hydrostatique $p$ (multiplicateur de Lagrange). Le potentiel se décompose en une partie déviatorique et une partie volumique :\n",
    "\n",
    "\n",
    "$\\Psi(\\mathbf{F}) = \\Psi_{\\text{iso}}(I_1, I_2) -p(J-1)$,\n",
    "\n",
    "\n",
    "où :\n",
    "- $I_1 = \\text{tr}(\\mathbf{C})$ (premier invariant),\n",
    "- $I_2 = \\frac{1}{2}\\left[(\\text{tr}(\\mathbf{C}))^2 - \\text{tr}(\\mathbf{C}^2)\\right]$ (second invariant),\n",
    "\n",
    "---\n",
    "\n",
    "### **1. Calcul de la contrainte de Piola-Kirchhoff 1 $(\\mathbf{P}$)**\n",
    "La contrainte $\\mathbf{P}$ est donnée par la dérivée du potentiel par rapport à $\\mathbf{F}$ :\n",
    "\n",
    "\n",
    "$\\mathbf{P} = \\frac{\\partial \\Psi}{\\partial \\mathbf{F}} = \\underbrace{\\frac{\\partial \\Psi_{\\text{iso}}}{\\partial \\mathbf{F}}}_{\\text{Partie isochore}}  - \\underbrace{p \\frac{\\partial (J - 1)}{\\partial \\mathbf{F}}}_{\\text{Contribution de la pression}}.$\n",
    "\n",
    "\n",
    "#### **(a) Partie isochore $(\\Psi_{\\text{iso}}$)**\n",
    "En utilisant la règle de dérivation des invariants, on peut montrer que :\n",
    "\n",
    "$\\frac{\\partial \\Psi_{\\text{iso}}}{\\partial \\mathbf{F}} = 2 \\mathbf{F} \\left( \\frac{\\partial \\Psi_{\\text{iso}}}{\\partial I_1} \\mathbf{I} + \\frac{\\partial \\Psi_{\\text{iso}}}{\\partial I_2} (I_1 \\mathbf{I} - \\mathbf{C}) \\right)$.\n",
    "\n",
    "\n",
    "#### **(c) Contribution de la pression $p$**\n",
    "La pression $p$ est un multiplicateur de Lagrange pour imposer $J = 1$ :\n",
    "\n",
    "$p \\frac{\\partial (J - 1)}{\\partial \\mathbf{F}} = p J \\mathbf{F}^{-T}$.\n",
    "\n",
    "\n",
    "---\n",
    "\n",
    "### **2. Expression finale de $\\mathbf{P}$**\n",
    "En combinant les deux contributions :\n",
    "\n",
    "$\\mathbf{P} = 2 \\mathbf{F} \\left( \\frac{\\partial \\Psi_{\\text{iso}}}{\\partial I_1} \\mathbf{I} + \\frac{\\partial \\Psi_{\\text{iso}}}{\\partial I_2} (I_1 \\mathbf{I} - \\mathbf{C}) \\right) - p J \\mathbf{F}^{-T}$.\n",
    "\n",
    "\n",
    "En quasi-incompressible ($J \\approx 1$) :\n",
    "\n",
    "$\\mathbf{P} \\approx 2 \\mathbf{F} \\left( \\frac{\\partial \\Psi_{\\text{iso}}}{\\partial I_1} \\mathbf{I} + \\frac{\\partial \\Psi_{\\text{iso}}}{\\partial I_2} (I_1 \\mathbf{I} - \\mathbf{C}) \\right) - p \\mathbf{F}^{-T}$.\n",
    "\n",
    "---\n",
    "\n",
    "### **3. Application à la traction uniaxiale**\n",
    "#### **(a) Champ de déformation**\n",
    "\n",
    "$\\mathbf{F} = \\begin{pmatrix}\n",
    "\\lambda & 0 & 0 \\\\\n",
    "0 & \\lambda_{\\text{trans}} & 0 \\\\\n",
    "0 & 0 & \\lambda_{\\text{trans}}\n",
    "\\end{pmatrix}, \\quad J = \\lambda \\lambda_{\\text{trans}}^2 \\approx 1 \\quad \\Rightarrow \\quad \\lambda_{\\text{trans}} \\approx \\lambda^{-1/2}$.\n",
    "\n",
    "\n",
    "#### **(b) Contrainte transverse nulle $(P_{22} = 0$)**\n",
    "La composante transverse de $\\mathbf{P}$ est :\n",
    "\n",
    "$P_{22} = 2 \\lambda_{\\text{trans}} \\left( \\frac{\\partial \\Psi_{\\text{iso}}}{\\partial I_1} + \\frac{\\partial \\Psi_{\\text{iso}}}{\\partial I_2} (I_1 - \\lambda_{\\text{trans}}^2) \\right) - p \\lambda_{\\text{trans}}^{-1} = 0$.\n",
    "\n",
    "Cette équation détermine $p$ :\n",
    "\n",
    "$p = 2 \\lambda_{\\text{trans}}^2 \\left( \\frac{\\partial \\Psi_{\\text{iso}}}{\\partial I_1} + \\frac{\\partial \\Psi_{\\text{iso}}}{\\partial I_2} (I_1 - \\lambda_{\\text{trans}}^2) \\right)$\n",
    "\n",
    "soit :\n",
    "\n",
    "$p = 2 \\lambda^{-1} \\left( \\frac{\\partial \\Psi_{\\text{iso}}}{\\partial I_1} + \\frac{\\partial \\Psi_{\\text{iso}}}{\\partial I_2} (I_1 - \\lambda^{-1}) \\right)$.\n",
    "\n",
    "#### **(c) Contrainte axiale ($P_{11}$)**\n",
    "\n",
    "$P_{11} = 2 \\lambda \\left( \\frac{\\partial \\Psi_{\\text{iso}}}{\\partial I_1} + \\frac{\\partial \\Psi_{\\text{iso}}}{\\partial I_2} (I_1 - \\lambda^2) \\right) + p \\lambda^{-1}$.\n",
    "\n",
    "En substituant $p$ et sachant que $\\lambda_{\\text{trans}} \\approx \\lambda^{-1/2}$:\n",
    "\n",
    "$P_{11} = 2 \\left( \\lambda - \\lambda^{-2} \\right) \\left( \\frac{\\partial \\Psi_{\\text{iso}}}{\\partial I_1} + \\lambda^2 \\frac{\\partial \\Psi_{\\text{iso}}}{\\partial I_2} \\right)$.\n",
    "\n",
    "---\n",
    "\n",
    "### **4. Résumé des équations clés**\n",
    "1. **Pression** :\n",
    "   \n",
    "   $p = 2 \\lambda^{-1} \\left( \\frac{\\partial \\Psi_{\\text{iso}}}{\\partial I_1} + \\frac{\\partial \\Psi_{\\text{iso}}}{\\partial I_2} (I_1 - \\lambda^{-1}) \\right)$.\n",
    "   \n",
    "2. **Contrainte axiale** :\n",
    "   \n",
    "   $P_{11} = 2 \\left( \\lambda - \\lambda^{-2} \\right) \\left( \\frac{\\partial \\Psi_{\\text{iso}}}{\\partial I_1} + \\lambda^2 \\frac{\\partial \\Psi_{\\text{iso}}}{\\partial I_2} \\right)$.\n",
    "\n",
    "3. **Allongement transverse** :\n",
    "   \n",
    "   $\\lambda_{\\text{trans}} = \\lambda^{-1/2} \\quad \\text{(à l'ordre dominant)}$.\n",
    "   \n",
    "\n",
    "---\n",
    "\n",
    "### **Conclusion**\n",
    "En quasi-incompressible :\n",
    "- La pression $p$ est déterminée par la condition $P_{22} = 0$.\n",
    "- La contrainte axiale $P_{11}$ dépend des dérivées de $\\Psi_{\\text{iso}}$ par rapport à $I_1$ et $I_2$.\n",
    "- L'allongement transverse est approximativement $\\lambda^{-1/2}$.\n",
    "\n",
    "Cette approche est générale et s'applique à tout potentiel dépendant de $I_1$ et $I_2$.\n",
    "\n",
    "\n",
    "---\n",
    "\n",
    "### **Potentiels à tester**\n",
    "\n",
    "1. **Néo-Hooke** :\n",
    "\n",
    "$\\Psi_{\\text{iso}}(I_1) = C_{10} (I_1-3)$\n",
    "\n",
    "2. **Mooney-Rivlin** :\n",
    "\n",
    "$\\Psi_{\\text{iso}}(I_1, I_2) = C_{10} (I_1-3) + C_{01} (I2-3)$\n",
    "\n",
    "3. **Polynomial** :\n",
    "\n",
    "$\\Psi_{\\text{iso}}(I_1) = C_{10} (I_1-3) + C_{20} (I_1-3)^2$\n",
    "\n",
    "4. **Demiray** :\n",
    "\n",
    "$\\Psi_{\\text{iso}}(I_1) = \\frac{C_1}{2 C_2} exp(C_2(I_1-3)-1)$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4539d279",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Paramètres optimaux de la fonction : [-5.99589338  5.02811653]\n",
      "Covariance :  [[ 0.0499671  -0.03077147]\n",
      " [-0.03077147  0.01913266]]\n"
     ]
    }
   ],
   "source": [
    "# Fonctions intermédiaires nécessaires à l'écriture de la fonction à identifier            \n",
    "\n",
    "def I1(x):\n",
    "    return ...\n",
    "\n",
    "def I2(x):\n",
    "    return ...\n",
    "\n",
    "def W1(x,...): #d(\\Psi_iso)/d(I1)\n",
    "    return ...\n",
    "\n",
    "def W2(x,...): #d(\\Psi_iso)/d(I2)\n",
    "    return ...\n",
    "\n",
    "# Contrainte de PK1\n",
    "def PK1(x,...):\n",
    "    return 2*(x-(1/x**2))*(W1(x,...)+(x**2)*W2(x,...))\n",
    "\n",
    "# Utiliser curve_fit pour ajuster la fonction aux données expérimentales\n",
    "# Vous devez fournir une estimation initiale des paramètres, avec une valeur initiale par paramètre à identifier\n",
    "\n",
    "initial_guess = [1,1] #à modifier\n",
    "parametres_optimaux, covariance = curve_fit(PK1, x_data, y_data_exp, p0=initial_guess)\n",
    "\n",
    "# Générer des données à l'aide des paramètres optimaux trouvés\n",
    "y_data_fit = PK1(x_data, *parametres_optimaux)\n",
    "\n",
    "# Afficher les résultats\n",
    "plt.scatter(x_data, y_data_exp, label='Données expérimentales')\n",
    "plt.plot(x_data, y_data_fit, label='Ajustement de fonction', color='red')\n",
    "plt.legend()\n",
    "plt.xlabel('Allongement (-)')\n",
    "plt.ylabel('Contrainte de PK1 (MPa)')\n",
    "plt.title('Ajustement de fonction aux données expérimentales')\n",
    "plt.show()\n",
    "\n",
    "# Afficher les paramètres optimaux trouvés\n",
    "print(\"Paramètres optimaux de la fonction :\", parametres_optimaux)\n",
    "print(\"Covariance : \", covariance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "55375cff-91dc-4ba9-816e-02654a25de1e",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
